Solve (5x5*55^25)

$$(5x5 \times { 55 }^{ 2 } 5)$$

Evaluate

$$75625x_{5}$$

Solution Steps

Calculate 55 to the power of 2 and get 3025.

$$5x_{5}\times 3025\times 5$$

Multiply 5 and 3025 to get 15125.

$$15125x_{5}\times 5$$

Multiply 15125 and 5 to get 75625.

$$75625x_{5}$$

Differentiate w.r.t. x_5

$$75625$$

Steps Using Definition of a Derivative

Calculate 55 to the power of 2 and get 3025.

$$\frac{\mathrm{d}}{\mathrm{d}x_{5}}(5x_{5}\times 3025\times 5)$$

Multiply 5 and 3025 to get 15125.

$$\frac{\mathrm{d}}{\mathrm{d}x_{5}}(15125x_{5}\times 5)$$

Multiply 15125 and 5 to get 75625.

$$\frac{\mathrm{d}}{\mathrm{d}x_{5}}(75625x_{5})$$

The derivative of ax^{n} is nax^{n-1}.

$$75625x_{5}^{1-1}$$

Subtract 1 from 1.

$$75625x_{5}^{0}$$

For any term t except 0, t^{0}=1.

$$75625\times 1$$

For any term t, t\times 1=t and 1t=t.

$$75625$$